Linear birth/immigration-death process with binomial catastrophes

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Abstract

In this paper, we study a birth/immigration-death processes under mild (binomial) catastrophes. We obtain explicit expressions for both the time-dependent (transient) and the limiting (equilibrium) factorial moments, which are then used to construct the transient and equilibrium distribution of the population size. We demonstrate that our approach is also applicable to multidimensional systems such as stochastic processes operating under a random environment and other variations of the model at hand. We also obtain various stochastic order results for the number of individuals with respect to the system parameters, as well as the relaxation time. Keywords: birth-death processes; catastrophes; time-dependent and equilibrium moments; equilibrium distribution; relaxation time
Original languageEnglish
Place of PublicationEindhoven
PublisherEurandom
Number of pages29
Publication statusPublished - 2015

Publication series

NameReport Eurandom
Volume2015006
ISSN (Print)1389-2355

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  • Cite this

    Kapodistria, S., Phung-Duc, T., & Resing, J. A. C. (2015). Linear birth/immigration-death process with binomial catastrophes. (Report Eurandom; Vol. 2015006). Eindhoven: Eurandom.